Extreme value theory is a crucial tool in finance and risk management for evaluating the tail risk of a distribution. We shall focus on the conditional tail expectation (CTE) among various risk measures, as it is regarded as more informative than the value-at-risk at a level q, the upper ( \(1-q\) )-quantile of the loss function. We consider a Pareto tail for the right-tail function and work with heavy tailed models, i.e. models with a positive extreme value index (EVI), quite common in finance. The link between the estimation of both the EVI and the CTE allows for the utilization of the class of EVI estimators based on the power mean of the log-excesses in CTE estimation. To assess the behaviour of this class in finite samples, Monte Carlo simulation experiments will be conducted.